Fertility and female employment reconsidered:

A macro-level time series analysis�

Henriette Engelhardt, Tomas K�ogel and Alexia Prskawetz

Max Planck Institute for Demographic Research,

Doberaner Str. 114, D-18057 Rostock, Germany

May 13, 2001

Abstract

Our paper examines causality and parameter instability in the long-

run relation between fertility and female employment. This is done

by cross-national comparison of macro-level time series data. By ap-

plying error correction models { a combination of Granger-causality

tests with recent econometric time series techniques { we �nd causal-

ity in both directions. This �nding is consistent with simultaneous

movements of both variables brought about by common exogenous

factors such as social norms, social institutions and �nancial incen-

tives. We �nd a signi�cant negative correlation until the 1970s, re-

spectively 1980s (depending on the country under investigation) and

an insigni�cant or weaker correlation afterwards. This result is consis-

tent with a recent hypothesis in the demographic literature according

to which changes in the institutional context like childcare availabil-

ity and attitudes towards working mothers might have reduced the

incompatibility between childrearing and female employment.

�For helpful comments and suggestions we would like to thank Juha Alho, Horst Entorf,

Ulf Christian Ewert, Tomas Frejka, Jan Hoem, Johannes Huinink, Stefan Klasen, Michaela

Kreyenfeld, Thomas Lindh, Warren Sanderson and participants at workshops in Heidelberg

and Rostock. We are especially grateful to Tom DiPrete who essentially contributed to

improve the exposition of the paper. The views expressed in this paper are the authors' own

views and do not necessarily represent those of the Max Planck Institute for Demographic

Research.

1

1 Introduction

The relationship between fertility and female labor force participation is a

long-standing question in demography. A negative association between these

two variables is mainly argued for as evidence for the incompatibility of

raising children and staying in the workforce in today's society where the

place of work and home are mostly spatially separated. Therefore, decreasing

fertility is associated with increasing female employment and rising female

employment is associated with falling fertility. Up to now, it is unclear

whether these mutual relations are causal in one or the other direction.

The question \What causes what?" received renewed attention in the

demographic literature during the last years. This renewed interest resulted

from recent studies which have shown that a simple cross-country correlation

coe�cient between the total fertility rate and the female labor force partici-

pation rate turned from a negative value before the 1980s to a positive value

thereafter. The question then arises whether there is a causal relationship at

all.

Several studies go beyond measures of correlation and explicitly attempt

to test for the existence and direction of causality between fertility and female

employment. Due to substantive and methodological shortcomings these

studies have found con icting results. Our paper aims to clarify the liter-

ature in three speci�c ways. First, we apply methods that are designed to

avoid the problem (referred to as \spurious regression" in the time series

literature) that frequently plagues the analysis of variables with trends and

that arguably a�icts existing e�orts to estimate the causal relation between

female labor force participation and fertility. Second, we estimate what are

called \error correction models" which are the appropriate models to test

for causality between stochastic trending time series. Third, we explicitly

test for \parameter instability," i.e., the possibility that the causal relation

between total fertility rate and female labor force participation has changed

over time.

Our results are twofold: (i) We �nd that there was a long-run causal re-

lation linking the total fertility rate and female employment until the end of

the 1970s or the begin of the 1980s (depending on the country of investiga-

tion). The results suggest that the causation was in both directions, but in

any case, we statistically rule out the possibility that the well-known corre-

lation between these variables was spurious. We argue that the bidirectional

causality is consistent with the view that comovements of fertility and fe-

2

male employment are caused by common exogenous factors. These factors

can be social norms and social institutions, but also opportunity costs of

childrearing and family income. (ii) Our empirical results show a signi�cant

negative correlation between fertility and female employment from the 1960s

to about the beginning of the 1970s for all countries of our study. How-

ever, for the non-Mediterranean countries in our sample the causal relation

becomes weaker (though still signi�cant negative) at about the end of the

1970s. Finally, we �nd considerable country-level heterogeneity in the rela-

tionship between fertility and female employment in the 1980s and 1990s. In

some countries, the relation becomes weaker to the point of insigni�cance,

while in others the relation remains signi�cantly negative.

Our results are supportive for a recent hypothesis in the demographic

literature according to which societal level responses have eased the incom-

patibility between childrearing and female employment in most developed

countries (Brewster and Rindfuss 2000; Rindfuss, Benjamin and Morgan

2000; Rindfuss and Brewster 1996). For the Mediterranean country in our

sample { Italy { we �nd the opposite result, that is, the negative correla-

tion between fertility and female employment becomes even stronger across

time. This �nding coincides with the argument in Rindfuss et al. (2000)

and Brewster and Rindfuss (2000) that we are only likely to see increasing

female employment no longer to depress fertility in those countries that suc-

ceeded in minimizing the incompatibility between childrearing and female

work. In Mediterranean countries this incompatibility between female em-

ployment and childrearing still persists.

The set up of our paper is as follows. In section 2 we �rstly discuss

the possible relationships between fertility and female employment from a

micro theoretical point of view. Secondly, we discuss the gap in the existing

macro-level time series literature that we aim to close with our paper. In

section 3 we describe the data and in section 4 we explain the econometric

methodology that is applied in the paper. We present the results in section

5 and conclude in section 6.

3

2 Theoretical and methodological considera-

tions

2.1 Micro explanations

At the individual level, numerous studies have shown a negative associa-

tion between fertility and female labor force participation (e.g., Lehrer and

Nerlove 1986; Brewster and Rindfuss 2000). On average, women in gainful

employment tend to have fewer children, and women with children spend

less time in the labor market. Weller (1977: 43) lists four possible expla-

nations for this negative association between fertility and female labor force

participation:

1. women's fertility a�ect their labor force participation;

2. women's labor force participation a�ect their fertility;

3. both women's fertility and their labor force participation a�ect each

other; and

4. the observed negative relationship is spurious and is caused by common

antecendents of both variables.

According to the mentioned role incompatibility hypothesis both women's

fertility and their labor force participation a�ect each other reciprocally be-

cause of the strain between mother and worker roles. Nothing in this hy-

pothesis suggests causality in one direction rather than the other (Lehrer

and Nerlove 1986).

From the point of view of economic theory fertility and female employ-

ment are simultaneously determined by the same basic economic variables.

More speci�cally, female labor market participation and fertility are both

choice variables which households choose simultaneously given their exoge-

nous constraints. If both variables uctuate to some extent synchronously,

then { according to the logic of economic theory { this must be caused entirely

by external variables which determine both variables exogenously. Examples

of such external variables are the real female wage, the unemployment rate

and { recently accepted in some work by economists { social norms.

Many researchers would not go as far as economic theory and would argue

that at least part of the correlation between fertility and female employment

4

is not determined by external variables. Some of these researchers view

fertility and female employment more as the result of a sequential decision

process rather than the result of a simultaneous decision problem. If these

variables are indeed the result of a sequential decision process, then it is quite

possible that one variable exogenously causes the other variable.

2.2 Macro studies

Given the discussed explanations of the fertility/employment nexus on the

micro level, it is no wonder that previous empirical research has mainly con-

centrated on micro-level data (for an extensive review of the micro literature

see Cramer 1980; Lehrer and Nerlove 1986; Spitze 1988). Nevertheless, with

existing cross-sectional as well as longitudinal survey data it is very di�-

cult to resolve the fertility/employment question since the empirical �ndings

depend on the underlying decision model (sequential or simultaneous), and

therefore on the applied statistical model. Furthermore, work intentions may

cause actual fertility behavior and fertility intentions may cause actual work

behavior, that is, future events may cause present behavior (Bernhardt 1993;

N�i Bhrolch�ain 1993). Macro-level studies { and especially cross-national com-

parisons { are an alternative way to resolve the fertility/employment puzzle

because they do not require the detailed individual-level data (see Rindfuss

and Brewster 1996: 262, who also stress the value of a cross-national assess-

ment). However, relationships at the individual and the aggregate level may

be di�erent (e.g., N�i Bhrolch�ain 1993).

Existing macro studies can be divided into studies which analyze macro-

level data on a cross-country basis and studies which apply methods of time-

series analysis. Various authors (Ahn and Mira 1999; Brewster and Rindfuss

2000; Esping-Andersen 1999; Rindfuss et al. 2000) �nd that in OECD coun-

tries the cross-country correlation between the total fertility rate (TFR) and

the female labor market participation rate (FLP ) turned from a negative

value before the 1980s to a positive value thereafter. The countries that now

have the lowest levels of fertility are those with relatively low levels of female

labor force participation and the countries with higher fertility levels tend

to have relatively high female labor force participation rates. Following the

graphical presentation in the literature (e.g., Rindfuss et al. 2000), Figure 1

illustrates this change for 12 selected OECD countries.1

1Countries included are Belgium, Canada, Finland, France, Italy, Japan, Norway, Swe-

5

Figure 1: Correlation between the total fertility rate and female labor force

participation rate, 1960-1994

1960 1965 1970 1975 1980 1985 1990-1

-0.5

0

0.5

1

year

corr

elat

ion

coef

fici

ent

Several recent papers have suggested a weakening link between fertility

and female employment due to greater availability of market child care, family

policies (such as state mandated maternity leave) and changing attitudes

towards working mothers (Brewster and Rindfuss 2000; Rindfuss et al. 2000;

Rindfuss and Brewster 1996). For that reason, they argue that changes in the

institutional context at the macro-level must have enabled women in some

countries to better combine work and childrearing.

The cross-section studies, however, do not explicitly address the causality

question. This is done in studies which apply formal Granger causality tests

to aggregate time-series in di�erent countries (Cheng 1996; Klijzing et al.

1988; Michael 1985; Zimmermann 1985). The basic logic underlying these

tests is quite simple: \We say, that [some time series] Yt is causing Xt if

we are better able to predict Xt using all available information than if the

information apart from Yt had been used" (Granger 1969: 428). Causality

between two time-series can be either unidirectional (X causes Y or the

reverse), bidirectional (X causes Y and the reverse { this is termed feedback)

den, Switzerland, United Kingdom, United States and West-Germany. The data sources

can be found in Appendix A.

6

or non existent in which case the two time series move independently or

contemporaneously.

Table 1: Summary of macro-level time-series studies

author method data results

Zimmermann (1985) modi�ed Granger / German time series TFR ! FLP

�rst di�erences 1960-79

Michael (1985) standard Granger / US time series TFR FLP

levels 1948-80 AFR! FLP

Klijzing et al. (1988) indirect Granger / Dutch survey data FER! LFP

�rst di�erences 1977-84 (FER LFP )

Cheng (1996) modi�ed Granger / US time series TFR! FLP

�rst di�erences 1948-93

Notes: TFR { total fertility rate; FLP { female labor force participation rate;

AFR { age-speci�c fertility rate; FER { lagged (by 10 months) number of

children born (per month); LFP { percentage of women participating in the labor

market (per month).

Table 1 provides a summary of empirical results of macro studies with

time series data. Analyzing German time-series from 1960-79 Zimmermann

(1985) concludes from a modi�ed Granger-causality test applied to �rst dif-

ferences of all variables that increasing female employment does not cause

decreasing fertility; rather the reduction in birth rate causes the increase in

female labor force participation. Applying standard Granger-causality tests

to the levels of US time-series data from 1948-80 Michael (1985) �nds that

female labor force participation positively causes fertility, but not the other

way around. However, this result seems to be sensitive to the de�nition of

fertility. With age-speci�c fertility rates Michael �nds that fertility nega-

tively a�ects female labor force participation, but not the other way around.

Klijzing et al. (1988) use monthly data from a Dutch survey for a seven-year

period (1977-84). They calculate the average value for each month in the

data of this survey and apply Sims' indirect Granger-causality test to the

�rst di�erences of these averages. They �nd that labor force participation

has no in uence on subsequent fertility decision-making and that fertility de-

cisions do have an impact on female labor force participation. However, with

standard Granger tests they �nd causality in both directions. Cheng (1996)

applies a modi�ed version of the Granger-causality method to �rst di�erences

of aggregate US data for 1948-93. He �nds unidirectional negative causality

7

running from fertility to female employment.

Obviously, the time series literature has not yet found an agreement nei-

ther on the presence nor on the direction of causality between fertility and

female employment. In our view, this might be due to two issues that are

not yet addressed in the literature. First, the literature has not yet taken

into consideration several important recent developments in the econometric

time series literature (see section 4). In particular, Michael (1985) does not

consider non-stationarity of the time series, that is whether the mean and/or

the variance of the time series are changing over time. This is problematic

because, if the time series are non-stationary, then there is the possibility

of \spurious" causality results. Cheng (1996), Klijzing et al. (1988) and

Zimmermann (1985) account for non-stationarity. However, by only apply-

ing Granger-causality tests to �rst di�erences, they refrain from the use of

valuable information about a possible long-run relationship between the vari-

ables.2 As a consequence, the results in these studies might be wrong.

Our paper contains two advances over these earlier papers that attempted

to determine causality. First, we use more recent data, which is important

because the relationship between TFR and FLP may have shifted in re-

cent years. Second, we employ more sophisticated econometric methods to

overcome de�ciencies in earlier e�orts. Besides the methodological issues

as related to the stationarity assumption of the time series we allow for a

further methodological correction. We consider the possibility of parameter

instability in the long-run relation between fertility and female employment

(as suggested by inspection of Figure 1) and structural breaks in the trend

of the variables. Clearly, it would be desirable to include in the regressions

socio-demographic variables that caused this change in behavior. However,

in our view this would be too complex { if not impossible { and, for that

reason, we approximate this change in behavior with the inclusion of dummy

variables. The use of such a \minimal" approach is a standard procedure in

applied econometrics.

2Though Cheng (1996) �nds absence of cointegration, that is, absence of a long-run

relation between fertility and female employment, we have shown that this results is not

robust. While he uses the correct Granger-causality method given this result, he uses a

unit root test on the OLS residuals of the cointegrating relation. We applied an error

correction model to the same data and found cointegration. We believe this to be due to

the well-known fact that error correction models are considered superior compared to the

residual based approach which tends to reject cointegration too often (see Kremers et al.

1992).

8

3 Data

We assembled annual time series of the total fertility rate (TFR) and female

labor force participation rate (FLP ).3 We assembled annual data from 1960-

94 for �ve European countries (France (FRA), West-Germany (FRG), Italy

(ITA), Sweden (SWE), and the United Kingdom (UK)). Moreover, we were

able to assemble annual data from 1948-1995 for the USA. Longer time series

are preferable because they increase the power of cointegration tests (Otero

and Smith 2000). For the purpose of comparison of the results of the USA

with the results of the European countries we also show the results for a

truncated time series for the USA that extends over 1960-94. For FLP we

choose the female labor force divided by the female population both of age

15 to 64. Hence, women of age 65 and older are not included in our measure

of FLP .

There are two possible measurement problems with our data. First, to

avoid problems arising from age structure changes we used as a measure of

fertility the total fertility rate (TFR) which constitutes an age standard-

ized measure of fertility (that is, the TFR is una�ected from age structure

changes). However, the FLP is not age standardized. Second, the FLP for

women 15 to 65 contains women of age 50 to 65 which cannot give births.

To check whether these two possible problems a�ected our empirical results,

we applied the same regressions also to the fertility rate of women of age

20-24 (respectively 25-34) and the female labor force participation rate of

women of age 20-24 (respectively 25-34) with annual US time series from

1948-1995.4 With age speci�c data one can avoid the two possible problems.

As a by-product it is possible to check whether age structure changes a�ect

the empirical results.

In Figure 2 and Figure 3 we plot the time series of TFR and FLP for

each country for 1960-94. As is well-known, the time series of TFR show

for most developed countries a kink in the 1960s. Some researchers argue

3See Appendix A for de�nition and source of data. In a few time series the value for a

single year was missing. In those cases we calculated the missing value as the average of

the year that preceded the missing year and the year that followed the missing year.4We neglected fertility of women of age below 20 and above 34 since the magnitude of

their fertility is relatively small. Unfortunately, data on fertility of women of age 25-29

and 29-34 were only available since 1976. Therefore, we restricted attention to the sum of

these two age groups. In addition, this data limitation made it impossible to construct an

age standardized measure of the female labor force participation rate (which would be an

alternative to avoid the �rst mentioned possible problem).

9

Figure 2: Time-series of the total fertility rate for six countries, 1960-94

1960 1965 1970 1975 1980 1985 19900

0.5

1

1.5

2

2.5

3

3.5

4

year

FRAFRGITASWEUKUSA

Figure 3: Time-series of female labor force participation rate for six countries,

1960-94

1960 1965 1970 1975 1980 1985 19900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

year

FRAFRGITASWEUKUSA

10

that this kink represents the di�usion of the use of the contraceptive pill

(e.g. Goldin and Katz 2000). Other researchers argue the kink is the result

of changing social norms. One can see that Italy is an exceptional case

since its fertility decline was very slow in comparison to most countries in

the developed world. The Swedish TFR shows a small hill around 1990.

The demographic literature o�ers some explanations for this hill which are,

however, outside of the scope of our paper (see, e.g., Andersson 1999, and

Hoem 1990, who explain the increase of the Swedish total fertility rate at the

end of the 1980s with newly enacted leave and wage compensation policies).

As is also well-known, the time series of FLP show a clear upwards trend

in most developed countries. Again Italy is an exception. There the rise

of female employment is rather modest. However, high education levels of

younger Italian women (not shown) seem to indicate a future change in the

FLP even in Italy. The Swedish FLP is distinguished by its relatively higher

level over the entire time period from 1960 to 1994.

We have opted to include Italy and Sweden in our set of countries since

each of them represents an extreme position in the spectrum of family poli-

cies and norms that may in uence the fertility/employment relation. The

exceptional behavior of the Italian time series is often explained with tradi-

tional norms and the view of the family as a private domain in which the

government does not intervene with many state services. On the other ex-

treme of a spectrum of family policy and norms is clearly Sweden. The policy

in the `nation of individuals' (Chesnais 1996; Hantrais 1997) tend to be both

supportive of women's desires and concerned with children's care. France

and the United Kingdom provide a somewhat weaker illustration of `nations

of individuals'. West-Germany as a `nation of families' shares a strong com-

mitment toward families, backed by monetary allowances for housing, child

bene�t packages, and well-paid maternal leave. To summarise: The time

series in Figure 2 and 3 show that our set of six countries is representative

for most developed countries.

4 Econometric methodology

Before introducing the speci�c method we apply, we shortly review some

of the recent econometric time series techniques that need to be taken into

account when testing for causality.

11

Cointegration

When estimating with time series data the relation between two trending

variables one often gets spurious regression results, that is, a seemingly sig-

ni�cant e�ect even though the variables are actually unrelated. An illus-

trative example is the fertility rate and the number of storks in a region.

Both variables have mostly a downward trend. Due to their trends, when re-

gressing the number of storks on the fertility rate with OLS one might �nd a

signi�cant positive e�ect even though it would be daring to argue that such a

causal relation exists in reality. Often detrending (that is, including a smooth

function of calendar time as a further element on the right hand side of the

regression equation) helps to eliminate spurious regression results. But as a

recent econometric literature (started by Granger and Newbold 1974) shows,

detrending does not help in case the variables are di�erence-stationary, also

labeled I(1). A series is di�erence-stationary if its mean and its variance

are constant over time after �rst di�erencing, but not in levels. We found

that FLP and TFR series appear to be di�erence stationary. Consequently,

analyses that attempt to estimate causation and that control for trends by

including a function of calendar time on the right side of the equation will not

generally give unbiased standard errors for inference of the causal relation.

If two time series are trending, the important question to determine is

whether the relation between these trends is \tight" enough so as to warrant

the conclusion that either there is a direct causal relationship between them,

or that there is some external force that is jointly determining both variables.

Cointegration tests can be applied to detect whether a relation between two

I(1) variables is `true' or spurious. These tests aim to detect synchronous

movements in deviations from the trend of both variables. More technically,

cointegration tests aim to detect whether there exists a linear combination

of two I(1) variables which is stationary (possibly after detrending). In case

such a stationary linear combination exists, the variables are said to be coin-

tegrated and the possibility of a spurious correlation due to trends can be

excluded.

Granger-causality

Granger (1969) introduced tests to detect causality between time series (hence-

forth labeled as Granger-causality test). The Granger causality test is typ-

ically based on the estimation of a vector autoregressive (VAR) model with

variables in levels or in �rst di�erences:

12

�Yt = �0 +

mYXi=1

�Y;i�Yt�i +

nYXj=1

�Y;j�Xt�j + uX;t; (1)

�Xt = �0 +

mXXk=1

�X;k�Yt�k +

nXXl=1

�X;l�Xt�l + uY;t; (2)

where �Zt = Zt � Zt�1; 8Z = Y;X; with all variables being in logarithms.

The �'s and �'s are constants, the m's and n's are the optimal numbers of

lags of the series Y and X and the ut's are serially uncorrelated random

disturbances with zero mean.5 For given values of the lag lengths (i.e, the

m's and n's) it can, for example, be tested, whether X Granger-causes Y

by testing the hypothesis H0: �Y;1 = �Y;2 = ::: = �Y;nY = 0 against the

alternative Ha: not H0. The joint signi�cance of the coe�cients can be

tested by a Wald test with the F-statistic.

Engle and Granger (1987) have shown that the Granger-causality test

can be seriously wrong if the time series are I(1) and cointegrated. For

that reason, the literare suggests to test �rst (with so-called unit root tests)

whether the variables are I(1). If the variables turn out to be I(1), the recent

literature suggest then to use a single error correction model (ECM) to test

for cointegration and causality upon application of , e.g., a method of Boswijk

(1994).

Testing for cointegration in a single error correction model

When trends are cointegrated, it follows that there is a long-run relation

between them. This long-run relation can be expressed in terms of what is

called an error correction model. An error correcting model explains changes

in one series in terms of three components: (1) random shocks, (2) recent

changes in the two series, and (3) an \error-correction" term that pushes the

series back into its long-run relation with the other series. The signi�cance

of the parameter for the error-correction term amounts to a statistical test

for the existence of a long-run causal relation between the two series. We

implement this error correction model below and we further allow for this

long-run relation to change historically, in order to test the hypothesis that

the employment-fertility con ict has changed in recent years at least for some

5Henceforth the ut's denote any disturbance term with zero mean.

13

countries in our sample. An ECM can be tested with OLS and is written in

the following form:6

�Yt = �0 + �Y Yt�1 + YXt�1 + 'Y t+

mYXi=1

�Y;i�Yt�i +

nYXj=1

�Y;j�Xt�j + uY;t;

(3)

where the �Y 's, �Y 's, �0, �Y ; Y and 'Y are constants, t is a trend term and

mY and nY are again the optimal number of lags of the �rst di�erences (we

choose mY and nY so that the Schwarz criterion was minimized, but limited

mY and nY to a maximum of 2). The purpose of the lags is to correct for

autocorrelation in the random disturbance term. Henceforth we include the

trend term in the ECM only if its coe�cient is signi�cant according to the

t-statistic (the t-statistic is reliable if Y and X are cointegrated).

Boswijk shows that one can test in (3) for cointegration between Y and

X with a joint Wald test of the hypothesis H0: �Y = Y = 0: In this

Wald test one has to compare the �2-statistic that results from a test of H0

with the critical values tabulated in Boswijk in Table B.1-B.5 (the tables are

for various cases, that is, with and without trend term in (3) and so forth).

Cointegration is accepted if the �2-statistic is larger than the relevant critical

value.

If there is absence of cointegration, then it is appropriate to test for

causality upon application of the standard Granger-causality test in �rst

di�erences, that is, to test for joint signi�cance of the lags in (1)-(2).

Testing for causality in a single error correction model

In case of cointegration, absence of weak exogeneity of X for Y implies long-

run causality of X for Y (Hall and Milne 1994). A test for weak exogeneity

in an ECM can be applied in two stages (Boswijk 1994). In the �rst stage

one may estimate the following equation with OLS:

Yt = Y + �YXt + �Y t + uY;t; (4)

Xt = X + �XYt + �Xt+ uX;t; (5)

6An analogous equation to (3) exist for �Xt as the dependent variable.

14

where the 's, �'s and �'s are constants. The relation in (4) and (5) is

labeled as long-run relation between Y and X. Note that this relationship

involves three elements: a slope coe�cient, a time trend, and a random error.

This relation is \long-term" in the sense that Yt � �YXt is stationary once

a smooth function of time (in our case, a linear time trend) is controlled

for. The crucial point here is that a speci�c linear combination of these

variables obeys an equilibrium relation in the long run. The residuals of

the estimates of (4) (that is, �̂Y;t = Yt � ̂Y � �̂YXt � �̂Y t) and (5) (that

is, �̂X;t = Xt � ̂X � �̂XYt � �̂Xt), where a hat on top of a variable denotes

the estimate of the corresponding parameter) are saved and labeled as error

correction terms. In the second stage the following equations are tested with

OLS:

�Yt = �0 + �Y �̂Y;t�1 +

mYXi=1

�Y;i�Yt�i +

nYXj=1

�Y;j�Xt�j + uY;t; (6)

�Xt = �0 + �X �̂X;t�1 +

mXXk=1

�X;k�Yt�k +

nXXl=1

�X;l�Xt�l + uX;t; (7)

where the �'s and �'s are constants, the �̂t�1's denote the lagged error cor-

rection term, the m's and n's are again the optimal numbers of lags of the

�rst di�erences chosen according to the Schwarz criterion. The variable X

(resp. Y ) is weakly exogenous for Y (resp. X), if �Y (resp. �X) is insignif-

icant according to the t-statistic. Otherwise long-run causality of X for Y

cannot be rejected. Intuitively, long-run causality implies that a deviation

in the long-run relation between X and Y , that is, �̂Y;t 6= 0 for some t, will

impact on the value of �Yt (and analogously for �̂X;t 6= 0).

If �Y as well as �X are signi�cant { which means that X long-run causes

Y as well as Y long-run causes X {, then one can interpret this as evidence for

that there exists a Z vector containing exogenous variables which is common

to Y and X and which \long-run causes" the cointegration relation of Y and

X.

Contrary to long-run causality, short-run causality ofX for Y prevails if in

(6) (resp. in (7)) the lags of �X (resp. of �Y ) are jointly signi�cant.7 How-

7X is termed strongly exogenous for Y , if there is absence of short-run causality and

long-run causality of X for Y and, in addition, uY;t in (6) and uX;t in (7) are uncorrelated

with each other (and analogously for Y in relation to X).

15

ever, in the subsequent analysis we only test for long-run causality (hence-

forth just labeled \causality"). This also agrees with Granger (1988) who

questions the usefulness of the concept of short-run causality for di�erence

stationary time series.8

In addition to merely testing for causality between two time series one

may also test for parameter instability in the long run relation between TFR

and FLP .

Testing for parameter instability in the long-run relation between

two variables within a single error correction model

Parameter instability occurs when the long-run relation between X and Y

changes. We allow two forms of parameter instability in our model. First, the

parametric relationship between X and Y (as represented by the coe�cient

for X) can change. Second, the linear time trend can change. To test for

parameter instability one may estimate the following equation with non-

linear least squares (NLS) (the estimation procedure { but not the test for

parameter instability { follows Boswijk 1994):

�Yt = �(Yt�1 � Y � �Y;1Xt�1 � �Y;2 DUMtB Xt�1 � �Y t) (8)

+

mYXi=1

�Y;i�Yt�i +

nYXj=1

�Y;j�Xt�j + uY;t;

with DUMtB =

�1 if t > tB0 otherwise

;

where �; Y ; �Y;1; �Y;2; �Y are constants. tB denotes the possible date of a

structural break in the slope parameter of X. The hypothesis of a break in

this slope parameter is accepted if �Y is signi�cant according to the t-statistic.

Inspired by a literature that suggests methods to test whether a time series is

di�erence-stationary (see Maddala and Kim 1998), we suggest to choose the

date of a possible break in the slope endogenously. More speci�c, we suggest

to estimate (8) for various values of tB and compare the corresponding t-

statistics for testing �Y = 0. The value of tB for which the absolute value of

the t-statistic is maximized may be chosen as the date of a possible break in

the slope. In case a break in the slope is accepted, we suggest to test the sign

8In case of stationary time series one can apply system (1)-(2) to test for causality

without the need to distinguish between short-run and long-run causality.

16

and the signi�cance of the correlation between X and Y before the break

and after it by testing the following equation with NLS:9

�Yt = �[Yt�1 � Y � �Y;1(DUM0 �DUMtB )Xt�1 (9)

��Y;2(DUMtB �DUMT )Xt�1 � �Y t]

+

mYXi=1

�Y;i�Yt�i +

nYXj=1

�Y;j�Xt�j + uY;t;

where@Yt�1

@Xt�1

j long�run =

��Y;1 for t < tB�Y;2 otherwise

;

and DUM0 = 1; 8t�[0; T ] and DUMT = 0; 8t�[0; T ], with the subscript 0

and respectively T as the dates at which the sample starts and respectively

ends. The (long-run) correlation between X and Y is signi�cant before the

break (resp. after the break) if �Y;1 = 0 (resp. �Y;2 = 0) is rejected according

to the t-statistic.

We have, for didactical reasons, deferred the exposition on how to test

for parameter instability to the end of this section. However, in practice

one needs to test for parameter instability in the �rst place, in order not to

distort the results of the cointegration and causality tests.

5 Empirical application

Prior to any test of causality we applied the Augmented Dickey-Fuller unit

root test to the time series of TFR and FLP . These tests showed that each

time series is di�erence-stationary. Therefore, we rule out the use of time

series models that attempt to estimate causal relation by simply regressing

one series on the other series, controlling for a time trend. Instead, an error-

correction model is called for. Therefore, we estimated equation (8) for (i)

�TFRt and alternatively (ii) �FLPt as the dependent variable. We found

a signi�cant trend in the long-run relation between TFR and FLP for each

country when we allow for breaks in the trend. Therefore, in the �rst step we

9Equation (9) is nothing else than equation (8) with the dummies rearranged. This

rearrangement does not change the content of the estimation results, but { in our view {

simpli�es the interpretation of the results. To give an example, in (9) the coe�cient in

front of the term (DUM0�DUMtB)Xt�1 represents the coe�cient of the slope before the

break (that is, from the date of the start of the sample to the date of the break).

17

determined the dates and the number of breaks in the trend for each equation.

To determine the exact date of a break in the trend, we followed the procedure

for determining endogenously the break in the slope as was explained in the

last section. That is, we compared the t-statistics of dummies for various

possible dates of the break and chose the date with the highest absolute value

of the t-statistic. Following Kim (1997), we chose the number of breaks in

the trend that minimized the Schwarz criterion. According to our estimates,

there were breaks in the trends in the long-run relation, with the timing of

the breaks varying somewhat by country. In the next step we tested for

instability in the long-run relation between TFR and FLP and tested for

an endogenous break in the slope parameter as explained in the previous

section.10

Our estimates of the stability of the slope coe�cient that links TFR and

FLP into a cointegrated trend has changed once for the countries under

investigation. The statistically optimal estimate for this break varies some-

what depending upon whether we model the long-run relation as an e�ect of

TFR on FLP or as an e�ect of FLP on TFR. We report the estimates of

these break points in Table 2. In our view, the important issue here is not the

exact timing of the break (we do not actually believe that the break occurred

at a single distinct point in history). Rather, the important point is that, at

least for some of the countries in our analysis, the long-run relation between

TFR and FLP has changed in recent history. Table 2 summarizes the dates

of breaks in the slope and suggests that for each country the correlation

between TFR and FLP has changed across time.

Next we tested for cointegration between TFR and FLP by estimating

equation (3) for (i) �TFRt and alternatively (ii) �FLPt as the dependent

variable (we include the breaks as determined in the step before). Table 3

summarizes the cointegration test results.11

10Once we allowed for a break in the correlation between TFR and FLP , then in a few

cases some breaks in the trend became insigni�cant according to the t-statistic and the

Schwarz criterion suggested too many breaks in the trend. In these few cases we abolished

the insigni�cant breaks in the trend.11As suggested by the results in Table 2 the coe�cient Y in equation (3) had in fact

to be split up into two coe�cients Y;1 and Y;2 with the former (latter) one referring to

periods before (after) the structural break. Therefore, we tested in (3) for cointegration

upon application of a Wald test of the joint hypothesis: H0: �Y = Y;1 = YY 2 = 0.

Alternatively, in case of insigni�cance of the slope after the break, one could estimate H 0

0:

�Y = Y;1 = 0: However, the results of testing H 0

0are the same as the results of testing

H0 and are therefore not shown in the paper.

18

Table 2: Endogenous dates of break in slope in time series regressions for six

countries, 1960-94, and additionally for the US, 1948-95 and US age speci�c

time series.

Dependent Variable

Country �TFRt �FLPtFRA 1976 1982

FRG 1985 1991

ITA 1981 1980

SWE 1970 1973

UK 1977 1986

USA 1970 1984

USA (1948-95) 1970 1977

USA20-24 (1948-95) 1971 1981

USA25-34 (1948-95) 1970 1967

Note: USA20-24 (respectively USA25-34) indicates that we apply age speci�c time series

of fertility and female labor force participation for women of age 20-24 (respectively 25-34).

Table 3 shows cointegration between TFR and FLP (mostly at the 1%

signi�cance level) for all countries with the only exception being the case of

Sweden when TFR is the dependent variable. Hence, there is strong evidence

for absence of spurious regression results for the association between TFR

and FLP in aggregate time series data.

In order to test for the direction of causality between TFR and FLP

we used the two stage procedure as explained in the previous section. For

illustration, assume there is one break in the slope and in the trend of each

time series. In this case we estimated in a �rst stage the following equations

with OLS:12

TFRt = TFR+�TFR;1(DUM 0�DUM tB;TFR)FLP t +

�TFR;2(DUM tB;TFR�DUMT )FLP t + (10)

�TFR;1(DUM 0�DUM t ~B;TFR)(t=100)+

�TFR;2(DUM t ~B;TFR�DUMT )(t=100);

12In these equations the dummies for the trend are rearranged in the same way as

are the dummies of the slope in (9). E.g. in (10) the coe�cient in front of the term

(DUM0�DUMt~B;TFR

)(t=100) represents the coe�cient of the trend between the start of

the sample and the date of the break in the trend t ~B;TFR.

19

Table 3: Test for cointegration between TFR and FLP in time series regres-

sions for six countries, 1960-94, and additionally for the US, 1948-95 and US

age speci�c time series.

Dependent Variable

Country �TFRt �FLPtFRA yes*** yes***

FRG yes** yes***

ITA yes*** yes***

SWE no yes***

UK yes*** yes***

USA yes** yes***

USA (1948-95) yes*** yes***

USA20-24 (1948-95) yes*** yes***

USA25-34(1948-95) yes*** yes***

Notes: *, **, *** 15%, 5%, 1% signi�cance level. \yes" means rejection of H0: no cointe-

gration.

FLP t = FLP+�FLP;1(DUM 0�DUM tB;FLP )TFRt +

�FLP;2(DUM tB;FLP�DUMT )TFRt + (11)

�FLP;1(DUM 0�DUM t ~B;FLP)(t=100)+

�FLP;2(DUM t ~B;FLP�DUMT )(t=100) ;

where the 's, �'s and �'s are constants, DUMtB;i ; 8i = TFR; FLP denotes

the break in the slope, DUMt ~B;i; 8i = TFR; FLP denotes the break in the

trend with the subscript tB;i and t ~B;i indicating the date of the break in

the slope and the trend respectively. As was the case in the cointegration

tests, we included in the estimations of equations (10) and (11) the breaks

which were signi�cant according to the estimations of (8). The residuals

that resulted from estimation of (10) (resp. (11)) were saved and used in the

estimation of (6) (resp. (7)) with �TFRt (resp. �FLPt) as the dependent

variable. Table 4 summarizes the results of the tests for causality.

The table shows clear evidence of causality in both directions for almost

all cases. The only country were we found no causality at all is Sweden. Note

that in case of Sweden when �TFR is the dependent variable we applied

the standard Granger-causality test in �rst di�erences because in this case

cointegration was rejected.

In our view Table 4 is, by and large, consistent with simultaneous move-

20

Table 4: Testing for causality between FLP and TFR for six countries, 1960-

94, and additionally for the US, 1948-95 and US age speci�c time series.

Country FLP ! TFR TFR! FLP

FRA yes*** yes**

FRG yes** no

ITA yes* yes**

SWE no no

UK yes** yes***

USA no yes**

USA (1948-95) yes*** yes**

USA20-24 (1948-95) yes*** yes***

USA25-34 (1948-95) yes*** yes*

Notes: *, **, *** 15%, 5%, 1% signi�cance level. \yes" means rejection of H0: weak

exogeneity.

ments of both variables brought about by common exogenous third vari-

ables. These third variables are presumably �nancial incentives, social norms

and/or social institutions which help to combine work and family.

Table 5 summarizes the �ndings from the estimates of the long-run rela-

tion in (9), that is, { for our illustrative example with one break in the trend

and for the case with TFR as the dependent variable:

TFRt�1 = ̂TFR + �̂TFR;1(DUM0 �DUMtB;TFR)FLPt�1 (12)

+�̂TFR;2(DUMtB;TFR �DUMT )FLPt�1

+�̂TFR;1 (DUM0 �DUMt ~B;TFR)(t=100)

+�̂TFR;2(DUMt ~B;TFR�DUMT )(t=100)

(and similar for the case with FLP as the dependent variable). The quanti-

tative estimation results are shown in Appendix B.

Our estimation results (Appendix B) show a signi�cant negative correla-

tion between TFR and FLP before the break in the slope for all countries in

all equations with the exception of Sweden in case with TFR as the depen-

dent variable. Furthermore, for all countries the magnitude of this relation

in the equation with TFR as the dependent variable exceeds the one in the

equation with FLP as the dependent variable. Table 5 shows that in almost

all cases (that is, for all countries almost always no matter whether TFR

or FLP is the dependent variable) the correlation between TFR and FLP

21

Table 5: Relation between TFR and FLP after the break in the slope for six

countries, 1960-94, and additionally for the US, 1948-95 and US age speci�c

time series.

�TFRt �FLPtCountry { 0 + { 0 +

FRA x x

FRG x x

ITA x x

SWE x

UK x x

USA x x

USA (1948-95) x x

USA20-24 (1948-95) x x

USA25-34 (1948-95) x x

Notes: { indicates that the relation between TFR and FLP after the break is signi�cant

negative and its magnitude exceeds the one before the break; 0 indicates that the relation

between TFR and FLP is either signi�cant negative and weaker as compared to the period

before the break, or insigni�cant; + indicates a signi�cant and positive relation between

TFR and FLP after the break. The signi�cance level is in any case the 15% level. For

each country we indicate with a cross the valid case.

becomes smaller in magnitude or even insigni�cant after the break. However,

the opposite holds for Italy where the negative relation between TFR and

FLP becomes even stronger after the break. Note that in case of Sweden

when TFR is the dependent variable we found no cointegration and accord-

ing to econometric theory there is no long-run relation in case of absence of

cointegration.

To conclude, we �nd for all non-Mediterranean countries evidence for

a signi�cant negative relation between TFR and FLP before the break in

the slope and an insigni�cant or signi�cant negative, but weaker relation

after the break. This �nding is consistent with the view in Rindfuss and

Brewster (1996), Rindfuss et al. (2000) and Brewster and Rindfuss (2000)

that changes in childcare availability and attitudes towards working moth-

ers might have reduced the incompatibility between childrearing and female

employment. Moreover, our empirical results show that for Italy the relation

between TFR and FLP did neither become insigni�cant nor weaker { ac-

tually it became even bigger in magnitude as compared to the period before

22

the break. This latter result is consistent with the view in Brewster and

Rindfuss and Rindfuss et al. that in the Mediterranean countries there were

not such changes of family policies and/or social norms which reduced the

incompatibility between childrearing and employment for women.13

A glance at the time plot of the Italian FLP might even give an expla-

nation for our �ndings. The time series clearly reveals that in Italy the FLP

for women fell from 1960 to 1965. It might be that in the year 1960 (and

possibly earlier) in Italy men's wage income was not enough to support the

family and so often women had also to participate in the labor market, but

could not restrict their fertility (for example, because at that time the con-

traceptive pill was not introduced). As in the early 1960s the wage income of

the men grew, often women had not anymore to work to support the family

and, as a consequence, reduced their employment. Clearly, such a mechanism

would reduce the correlation between TFR and FLP in the initial periods

of our sample.

6 Conclusion

In this study we applied recent econometric time series techniques to test

for causality between fertility and female employment with macro-level time

series data of six developed countries. Compared to previous research we

introduced two new methodological elements: (i) we allowed for parameter

instability and (ii) we used an error correction model.

The existing literature mostly found unidirectional causation and con-

icting results on the direction between fertility and female employment. In

the light of our empirical results { which show causality in both directions {

we suggest that previous research tended to reject causality too often. The

failure to account for parameter instability (either in the long-run relation be-

tween fertility and female employment and/or the trend of each time series)

may partly explain why previous research rejected causality too often (see

Table 1). Moreover most of the previous research either ignored di�erence-

stationarity or applied Granger-causality tests to the �rst di�erences of the

time series without testing for cointegration.

Our result of causation in both directions indicates that ignoring di�erence-

stationarity did probably not lead to wrong causality results since this failure

13We would expect for other Mediterranean countries (such as Greece, Spain and Por-

tugal) the empirical results to be similar to the result for Italy.

23

tends to �nd \spurious" causality rather than to reject causality too often

(indeed Michael 1985, who applies Granger-causality tests to the levels and

ignores di�erence-stationarity as well as parameter instability, �nds some ev-

idence for causality in both directions). Nevertheless, in case of di�erence

stationary time series an error correction model is by far the most appropriate

model and testing for cointegration is imperative in this case.

The application of a Granger-causality test to the �rst di�erences of the

time series is a special case of the application of an error correction model.

More speci�cally, it is a Granger-causality test without the inclusion of the

error correction term. However, not including the error correction term might

lead to serious problems because the error correction term contains the in-

formation about a possible long-run relation between fertility and female

employment. For that reason, Granger-causality tests applied to �rst dif-

ferences can only test for \instantaneous causation" and the information on

long-run causation is lost in this framework. From a statistical point of view,

this loss of information might be an additional explanation why the existing

literature tended to reject causality too often. From a substantive point of

view, if the correlation between fertility and female employment is the re-

sult of intentions (as, for example, economists would argue), then testing for

instantaneous causation is not useful. Clearly, if individuals \decide" about

their number of children, their timing of childbearing and their labor market

participation, then a respond to shocks takes time and, therefore, a test of

long-run causality seems much more useful.

Allowing for parameter instability not only prevented us from rejecting

causality too often. Omission of a break in the trend can also lead to biased

estimates of the coe�cient of the relationship between fertility and female

employment. Obviously, the same is true for the failure to account for insta-

bility in the correlation between fertility and female employment. Michael

(1985), for example, �nds a positive e�ect from female employment on fer-

tility with macro-level data. We also found in our empirical applications a

positive coe�cient for some countries when we did not account for structural

breaks (the results are not shown). However, when we accounted for param-

eter instability, we found for all countries a negative coe�cient before the

break. Empirical results that show a positive correlation between fertility

and female employment already in the 1960s and the 1970s might { in our

view { indicate biased estimates due to the failure to account for parameter

instability (it is possible that for Nordic countries the situation is di�erent).

Besides the improvements of the estimation results, accounting for pa-

24

rameter instability is also an interesting �nding in its own right. Most im-

portantly, allowing for instability of the correlation between fertility and

female employment revealed that for all non-Mediterranean countries the

correlation became weaker over time. This result with time series data com-

plements and supports recent studies which found for OECD countries that

the cross-country correlation between fertility and female employment turned

from a negative value before the 1980s to a positive value thereafter. Our

empirical �nding supports therefore the view of a recent demographic liter-

ature which argues that societal level responses reduced the incompatibility

between fertility and female employment.

While those latter studies as well as our study do not distinguish between

full and part-time employment, the availability of part-time employment is

clearly a further element of societal level responses which also might have

reduced the incompatibility between childrearing and female labor market

participation. As more data about availability of part-time employment will

become accessible in the future, we suggest for future work to estimate the

contribution of availability of part-time employment to the weakening asso-

ciation between fertility and female employment.

To illustrate the importance to apply more sophisticated econometric

methods, as suggested in our paper, we conclude by showing the results of a

simple OLS regression of TFR on FLP with a trend and a constant included

on the right hand side.14 We applied this regression to all six countries of

our sample and for the time interval 1960-94.

Table 6: OLS regressions of TFR on FLP

Country Coe�cient of FLP P-value of coe�cient of FLP

FRA {2.47 0.00

FRG 2.38 0.00

ITA {0.85 0.00

SWE {1.73 0.00

UK {0.40 0.73

USA {4.11 0.00

Note: All regressions include a constant and a trend.

Though for �ve out of our six countries the OLS coe�cients on FLP are

14Results from simple OLS regressions of FLP on TFR with a trend and a constant

included on the right hand side are very similar.

25

negative (cf. Table 6), a closer look at the level and the signi�cance of the

estimates reveals several counterintuitive results. The positive coe�cient on

FLP for West-Germany seems clearly against the general predictions of de-

mographic theories. Though recent demographic �ndings suggest a reduction

in the incompatibility between childrearing and female employment, none of

these theories actually predicts a positive causal e�ect from FLP on TFR.

Comparing the estimates for Italy, Sweden and UK implies the lowest incom-

patibility between childrearing and female employment for the UK (where

the coe�cient on FLP is insigni�cant), followed by Italy and Sweden ranking

last. Again, these results are against the general �ndings in the demographic

literature so far where Sweden is always regarded as the country with the

highest compatibility between childrearing and female employment. Finally,

according to the OLS estimates the USA turns out to be the country with

the by far strongest incompatibility between childrearing and female employ-

ment in our sample. Again, one would rather expect Italy to be a country

that ranks lowest on the incompatibility between childrearing and female

employment. To conclude: The empirical results in our paper are much

more intuitive and are supported by the view of a recent demographic liter-

ature which argues that societal level responses reduced the incompatibility

between fertility and female employment. The importance to apply more

sophisticated econometric methods that go beyond simple OLS regressions

is therefore evident.

26

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Appendix A: The data

1. TFR: total fertility rate

De�nition: Sum of age speci�c fertility rates

Data sources: German Federal Statistical O�ce, section population

and labor force (in case of West Germany), New Cronos CD-Rom (from

Eurostat) (1998)(in case of Western European countries other than

West-Germany) and the Demographic Yearbook of The United Nations

CD-Rom (1997)(for all other countries).

2. FLP : female labor force participation in female population of age 15

to 64

De�nition: Logarithm of female labor force including female unem-

ployed divided by logarithm of female population of age 15 to 64

Data source: Comparative welfare states data set http://www.lis.ceps.lu/

(except West-Germany after 1989 and US where the sources are: Ger-

man Federal Statistical O�ce, microcensus and US Bureau of Labor

statistics http://stats.bls.gov/).

30

AppendixB:Estimationresultsoflong-runrelation

15

FRA

TFRt�

1=�

0:19�

1:66�

�

�

(DUM59�

DUM76)FLPt�

1�

1:32�

�

�

(DUM76�

DUM94)FLPt�

1�

0:55�

�

�

(DUM59�

DUM73)(t=100)

(�

8:42)

(�

5:41)

(�

3:30)

�

1:01�

�

�

(DUM73�

DUM76)(t=100);

(�

4:67)

FLPt�

1=�

0:68�

0:17�

�

�

(DUM59�

DUM82)TFRt�

1�

0:05(DUM82�

DUM94)TFRt�

1+0:59�

�

�

(DUM59�

DUM82)(t=100)

(�

8:34)

(�

1:15)

(9:64)

+0:32�

�

�

(DUM82�

DUM89)(t=100)+0:43�

�

�

(DUM82�

DUM94)(t=100):

(4:97)

(7:94)

FRG

TFRt�

1=�

0:05�

1:30�

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(DUM59�

DUM85)FLPt�

1�

0:69(DUM85�

DUM94)FLPt�

1�

1:67�

�

�

(DUM68�

DUM85)(t=100),

(�

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(�

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(�

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FLPt�

1=�

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(DUM59�

DUM91)TFRt�

1+0:11�

(DUM91�

DUM94)TFRt�

1�

0:15�

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(DUM65�

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(�

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(1:64)

(�

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+0:14�

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(DUM79�

DUM85)(t=100)+0:25�

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DUM89)(t=100)+0:55�

�

�

(DUM89�

DUM90)(t=100)+0:32�

�

�

(DUM90�

DUM94)(t=100):

(5:64)

(8:63)

(8:25)

(6:40)

15Asmentionedbefore,inourapplicationwe�ndforsomecountriesmorethanonebreakinthetrend.Thenotationfor

thecasewithmultiplebreaksinthetrendisastraightforwardextensionofthenotationusedinthetext(forexample,the

coe�cientinfrontoftheterm(DUM

64�

DUM

78)(t=100)representsthecoe�cientofthetrendfrom1965to1978).Moreover,

weexcludedintheestimationequationthetrendforaparticulartimeintervalifinpriorestimationsthetrendwasinsigni�cant

forthattimeinterval(accordingtoatleastthe15%signi�cancelevel).

31

ITA

TFRt�

1=0:30�

0:85�

�

(DUM59�

DUM81)FLPt�

1�

1:05�

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(DUM81�

DUM94)FLPt�

1�

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(DUM64�

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(�

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(�

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(�

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�

2:69�

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�

(DUM74�

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2:19�

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(DUM87�

DUM94)(t=100);

(�

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(�

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FLPt�

1=�

0:67�

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(DUM59�

DUM80)TFRt�

1�

0:70�

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(DUM80�

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1+0:30�

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(DUM74�

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(�

8:48)

(�

6:40)

(�

3:62)

�

0:28�

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(DUM92�

DUM93)(t=100):

(�

2:13)

SW

E

FLPt�

1=�

0:26�

0:35�

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�

(DUM59�

DUM73)TFRt�

1�

0:17�

(DUM73�

DUM94)TFRt�

1+0:38�

�

�

(DUM67�

DUM91)(t=100):

(�

4:10)

(�

1:58)

(5:13)

UK

TFRt�

1=0:13�

1:25�

�

�

(DUM59�

DUM77)FLPt�

1�

0:97�

�

�

(DUM77�

DUM94)FLPt�

1�

0:46�

�

�

(DUM64�

DUM71)(t=100)

(�

7:15)

(�

3:34)

(�

3:27)

�

1:35�

�

�

(DUM71�

DUM77)(t=100)�

0:26�

�

(DUM77�

DUM86)(t=100);

(�

8:97)

(�

2:59)

FLPt�

1=�

0:75�

0:10�

�

�

(DUM59�

DUM86)TFRt�

1�

0:04(DUM86�

DUM94)TFRt�

1+0:80�

�

�

(DUM59�

DUM94)(t=100):

(�

2:95)

(�

1:40)

(8:18)

32

USA(1960-94)

TFRt�

1=0:21�

1:10�

�

�

(DUM59�

DUM70)FLPt�

1�

0:80�

�

�

(DUM70�

DUM94)FLPt�

1�

0:77�

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�

(DUM64�

DUM76)(t=100)

(�

5:25)

(�

2:86)

(�

3:42)

�

0:45�

�

�

(DUM86�

DUM94)(t=100);

(�

3:42)

FLPt�

1=�

0:43�

0:30�

�

�

(DUM59�

DUM84)TFRt�

1�

0:21�

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�

(DUM84�

DUM94)TFRt�

1+0:20�

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(DUM64�

DUM76)(t=100)

(�

6:69)

(�

5:52)

(2:09)

+0:51�

�

�

(DUM76�

DUM94)(t=100):

(5:34)

USA(1948-95)

TFRt�

1=0:39�

0:79�

�

�

(DUM47�

DUM70)FLPt�

1�

0:35�

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(DUM70�

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1+1:28�

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(DUM52�

DUM61)(t=100)

(�

7:46)

(2:34)

(�

3:72)

�

0:53�

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�

(DUM64�

DUM73)(t=100)+0:32�

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�

(DUM86�

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(�

3:24)

(3:79)

FLPt�

1=�

0:91�

0:09�

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(DUM47�

DUM77)TFRt�

1�

0:02(DUM77�

DUM95)TFRt�

1+1:30�

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(DUM47�

DUM89)(t=100)

(�

4:09)

(�

0:68)

(19:91)

+1:23�

�

�

(DUM89�

DUM95)(t=100):

(20:72).

33

USA20-24(1948-95)

FERt�

1=�

2:21�

0:91�

�

�

(DUM47�

DUM71)FLPt�

1�

0:03(DUM71�

DUM95)FLPt�

1+1:09�

�

�

(DUM53�

DUM61)(t=100)

(�

9:64)

(�

0:16)

(4:58)

�

0:99�

�

�

(DUM64�

DUM71)(t=100);

(�

5:22)

FLPt�

1=�

1:27�

0:31�

�

�

(DUM47�

DUM81)FERt�

1�

0:30�

�

�

(DUM81�

DUM95)FERt�

1�

0:94�

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(DUM51�

DUM53)(t=100)

(�

14:65)

(�

13:87)

(�

1:91)

+0:73�

�

�

(DUM53�

DUM89)(t=100)+0:60�

�

�

(DUM89�

DUM95)(t=100):

(10:55)

(9:41).

USA25-34(1948-95)

FERt�

1=�

1:88�

0:56�

�

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(DUM47�

DUM70)FLPt�

1�

0:32�

�

�

(DUM70�

DUM95)FLPt�

1+1:28�

�

�

(DUM50�

DUM61)(t=100)

(�

8:30)

(2:89)

(4:23)

�

0:64�

�

�

(DUM64�

DUM76)(t=100)+0:29�

�

�

(DUM84�

DUM95)(t=100);

(�

4:80)

(3:73)

FLPt�

1=�

2:40�

1:06�

�

�

(DUM47�

DUM67)FERt�

1�

0:96�

�

�

(DUM67�

DUM95)FERt�

1+1:24�

�

�

(DUM47�

DUM90)(t=100):

(�

7:31)

(�

7:58)

(7:79)

Notes:*,**,***15%,5%,1%signi�cancelevel,t-statisticsinparenthesisand

DUM

i=

�1

if

t>

i

0

otherwise

;8

i�[60;94];FER

representstheagespeci�cfertilityrate.

34